Exponential Hilbert series and hierarchical log-linear models

Autor:	Johnson, Wayne A.
Rok vydání:	2022
Předmět:	Mathematics - Combinatorics Mathematics - Statistics Theory
Druh dokumentu:	Working Paper
Popis:	Consider a hierarchical log-linear model, given by a simplicial complex, $\Gamma$, and integer matrix $A_\Gamma$. We give a new characterization of the rank of $A_\Gamma$ given by a logarithmic transformation on the exponential Hilbert series of $\Gamma$. We show that, if each random variable in $X$ has the same number of possible outcomes, then this formula reduces to a simple description in terms of the face vector of $\Gamma$. If $\Gamma$ further satisfies the Dehn-Sommerville relations, then we give an exceptionally simple formula for computing the rank of $A_\Gamma$, and thus the dimension and the number of degrees of freedom of the model. Comment: Corrected typo in Corollary 2. Added comment on cyclic models
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.03765 Zobrazit plný text záznamu View this record from Arxiv